Potential of a conductor in a non-uniform E field

[serverxeon]

imagine there is a positive pt charge somewhere in space. so the E field due to this pt charge, falls off with distance.


now, i place a conducting rod parallel to the field some distance away,
such that one end of the rod is at V_A and another end is V_B
(where V_A > V_B)

we also know that there can be no net E-field in a conductor. so potential must be constant throughout a conductor.

my question is. what is the potential?? V_A or V_B? or what?

 

[technician]

The potential of the conducting rod will be constant. One end will not be at a different potential to the other end.
-charge (electrons) will be attracted to the end nearest the + charge and the end further from the + charge will be + charged.

 

[serverxeon]

Yes I know the mechanism.

My question is what is the numerical potential?

Assume the potential due to the external field at pt A is 10V,
the potential due to the external field at pt B is 5V,

then what is the potential anywhere in the rod?